Comments for MEDB 5502, Week 03
Topics to be covered
What you will learn
Indicator variables for three or more categories
Multiple factor analysis of variance
Checking assumptions of analysis of variance
Interactions in analysis of variance
Interactions in analysis of covariance
Interactions in multiple linear regression
The general linear model
To be determined
Review oneway analysis of variance
\(H_0:\ \mu_1=\mu_2=...=\mu_k\)
\(H_1:\ \mu_i \ne \mu_j\)
for some i, j
Reject
\(H_0\)
if F-ratio is large
Note: when k=2, use analysis of variance or t-test
Full moon data
Admission rates to mental health clinic before, during, and after full moon.
One year of data
Boxplot of full moon data
Descriptive statistics
Analysis of variance table
Tukey post hoc
Creating indicator variables
Running general linear model with all indicator variables
Analysis of variance with first and second indicators
9
Parameter estimates, 1 of 3
11.458 - 13.417 = -1.959
10.917 - 13.417 = -2.5
Parameter estimates, 2 of 3
11.458 - 10.917 = 0.541
13.417 - 10.917 = 2.5
10.917 - 11.458 = -0.541
13.417 - 11.458 = 1.959
\(\ \)
Reference category, the category associated with the indicator variable left out of the model.
Using moon as a fixed factor
Removing the unneeded rows
Parameter estimates using Moon as a fixed factor
Live demo, Multiple factor analysis of variance
Break #1
What you have learned
Indicator variables for three or more categories
What’s coming next
Multiple factor analysis of variance
Mathematical model
\(Y_{ijk} = \mu + \alpha_i + \beta_j +\epsilon_{ijk}\)
i=1,…,a levels of the first categorical variable
j=1,…,b levels of the second categorical variable
k=1,…,n replicates with first and second categories
\(\ \)
\(H_0:\ \alpha_i=0\)
for all i
\(\ \)
\(H_0:\ \beta_j=0\)
for all j
16
17
18
19
20
21
Live demo, Multiple factor analysis of variance
Break #2
What you have learned
Multiple factor analysis of variance
What’s coming next
Checking assumptions of analysis of variance
Assumptions
Normality
Equal variances
Independence
22
23
Live demo, Checking assumptions of analysis of variance
Break #3
What you have learned
Checking assumptions of analysis of variance
What’s coming next
Interactions in analysis of variance
1
2
3
4
Live demo, Interactions in analysis of variance
Break #4
What you have learned
Interactions in analysis of variance
What’s coming next
Interactions in analysis of covariance
5
6
7
8
Live demo, Interactions in analysis of covariance
Break #5
What you have learned
Interactions in analysis of covariance
What’s coming next
Interactions in multiple linear regression
9
10
Live demo, Interactions in multiple linear regression
Break #6
What you have learned
Interactions in multiple linear regression
What’s coming next
The general linear model
Slide 04-07
Live demo, The general linear model
Break #7
What you have learned
The general linear model
What’s coming next
To be determined
Slide 04-08
Live demo, To be determined
Summary
What you have learned
Indicator variables for three or more categories
Multiple factor analysis of variance
Checking assumptions of analysis of variance
Interactions in analysis of variance
Interactions in analysis of covariance
Interactions in multiple linear regression
The general linear model
To be determined
Additional topics??